Question

15 points

The side lengths of four triangles are shown in the table. Select all the triangles that are right triangles.

Answer 1

9514 1404 393

Answer:

I, III

Explanation:

You know from your study of the Pythagorean theorem that a triangle with sides 3, 4, and 5 will be a right triangle. Any scaled version of this triangle will also be a right triangle, so it is helpful to learn to recognize when scaled values of these numbers are used.

I -- the scale factor for a 3-4-5 right triangle is 2/10

II -- no isosceles right triangle has integer side lengths. (not a right triangle)

III -- the scale factor for a 3-4-5 right triangle is 1/13

IV -- the lengths do not form a triangle

Triangles I and III are right triangles.

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Additional comment

The sides of an isosceles right triangle have the ratios 1 : 1 : √2. The square root of 2 is irrational. No scaled version of this triangle can have rational side lengths.